Analysis and Comparison on Image Restoration Algorithms Using … · 2019. 7. 1. · Image restoration assures good insights of image when it is subjected to further techniques of

Analysis and Comparison on Image Restoration Algorithms Using

MATLAB

Admore Gota School of Electronics Engineering, Tianjin University of Technology and Education (TUTE),

Tianjin P.R China.

Zhang Jian Min School of Electronics Engineering, Tianjin University of Technology and Education (TUTE),

Tianjin P.R China.

Abstract

TheImage restoration is the recovery of an

image that has been degraded by blur and noise.

Degradation typically involves blurring of the

original image and corruption noise. The recovery

of an original image from degraded observations is

of paramount importance and can find its

application in several scientific areas including

medical and diagnostics, military

surveillance,satellite and astronomical imaging,

remote sensing, authentication automated industry

inspection and many areas. Image restoration

assures good insights of image when it is subjected

to further techniques of image processing.

Presentation of the results and comparisons of the

restoration algorithms namely Weiner Filter, the

Regularized filter and Lucy-Richardson as

implemented in Matlab. This is done using an

image that is degraded by motion blur with

Gaussian, Salt and Pepper and Speckle noise

models respectively and restoration of same image

using various algorithms mentioned above. Image

restoration algorithms, distinguish themselves from

enhancement methods in that they are based on

models for degrading process and for the ideal

image. The image restoration methods in this paper

fall under the class of linear spatially invariant

restoration filters. Degradation typically involves

blurring of the original image and corruption

noise.

1. Introduction

Visual information transmitted in the form of

digital images is becoming a major method of

communication in the modern age. Images are

produced to record or display useful information.

However, due to imperfections in the imaging and

capturing process, the recorded image invariably

represents a degraded version of the original scene.

The undoingof these imperfections is crucial to

many of the subsequent image processing tasks. A

wide range of degradations such as noise,

geometrical degradations, illumination and color

imperfections and blur. This paper concentrates on

basic methods for removing blur and noise, in this

case Gaussian, Salt and Pepper and Speckle noise

from recorded and spatially images.

The field of image restoration which is sometimes

referred to as image deblurring or image

deconvolution is concerned with the reconstruction

or estimation of uncorrupted image from blurred

and noisy one. Image restoration is associated with

minimizing or even removing artifacts due to

blurring and noise. Blurring which is a linear form

of degradation can occur due to camera

defocussing or due to motion. This project

concentrates on the Analysis and Comparison of

methods of image restoration algorithms.

2. The Objectives of the project are: To find out a suitable highly accurate

restoration algorithm to filter and remove

the degradation on an image using Matlab

simulation.

To investigate the strength and limitations

of each image restoration algorithm.

To find a suitable algorithm with high

performance of filtering and doing a great

job of restoring the image.

To generate an estimate of the original

image prior to the degradation.

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Vol. 2 Issue 12, December - 2013

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3. Blur Models

In most cases the blurring of images is a spatially

continuous process. Since identification and

restoration algorithms are always based on spatially

discrete images, we present the blur models in their

continuous forms. The imperfections in the image

formation process are modelled as passive

operations on the data that is no energy is absorbed

or generated. Following is the presentation of four

common point-spread functions, which are

encountered regularly in practical situations of

interest.

A.No Blur

In case the recorded image is imaged perfectly, no

blur will be apparent in the discrete image.

B.Linear motion blur

Many types of motion blur can be distinguished all

of which are due to relative motion between the

recording device and the scene. This can be in the

form of a translation, a rotation, a sudden change of

scale. Here only the important case of a global

translation will be considered.

C.Uniform Out of focus blur

When a camera images a 3-D scene onto a 2-D

imaging plane, some parts of the scene are in focus

while other parts are not. If the aperture of the

camera is circular, the image of any point source is

a small disk, known as the circle of confusion

(COC).

D.Atmospheric turbulence blur

Atmospheric turbulence is a severe limitation in

remote sensing. Although the blur introduced by

atmospheric turbulence depends on a variety of

factors such as temperature, wind speed and

exposure time, for long-term exposures the point

spread function can be described reasonably well

by a Gaussian function.

4. Noise Models

The noise commonly present in an image. Note that

noise is undesired information that contaminates

the image. In the image de-noising process,

information about the type of noise present in the

original image plays a significant role. Typical

images are corrupted with noise modelled with

either a Gaussian, or salt and pepper distribution.

Another typical noise is a speckle noise, which is

multiplicative in nature. Noise is present in an

image either in an additive or multiplicative form.

A.Gaussian Noise

Its evenly distributed over the signal. This means

that each pixel in the noisy image is the sum of the

true pixel value and a random Gaussian distributed

noise value. As the name indicates, this type of

noise has Gaussian distribution, which has a bell-

shaped probability distribution function given by,

Where g represents the gray level is the mean or

average of the function, and 𝜎 𝑖𝑠 the standard

deviation of the noise. Graphically it is represented

as shown in Figure 1.When introduced into an

image, Gaussian noise with zero mean and variance

as 0.05 would look as in figure 2a. Figure 2b

illustrates the Gaussian noise with mean (variance)

as 1.5 (10) over a base image.

Figure 1.Gaussian Distribution

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(a) (mean=0, variance =0.05)

(b) (mean=1.5, variance=10)

Figure 2: Image degraded by Gaussian noise

with different mean and variance values

B. Salt and Pepper Noise

Is an impulse type of noise, which is also referred

to as intensity spikes. This is caused generally due

to errors in data transmission. It has only two

possible values, a and b. The probability of each is

typically less than 0.1. The corrupted pixels are set

alternatively to the minimum or to the maximum

value, giving the image a salt and pepper like

appearance. Unaffected pixels remain unchanged.

For an 8-bit image, the typical value for pepper

noise is 0 and for salt noise 255.The salt and pepper

noise is generally caused by malfunctioning of

pixel elements in the camera sensors, faulty

memory locations, or timing errors in the

digitization process. The probability density

function for this type of noise is shown in Figure 3.

Salt and pepper noise with a variance of 0.05 is

shown in Figure 4.

Figure 3: PDF for Salt and Pepper noise.

C. Speckle Noise

Is a multiplicative noise. This type of noise occurs

in almost all coherent imaging systems such

aslaser, acousticsand SAR (Synthetic Aperture

Radar) imaginery. The source of this noise is

attributed to random interference between the

coherent returns. Fully developed speckle noise has

the characteristic of multiplicative noise. Speckle

noise follows a gamma distribution and is given as

The where variance is a2α andgis the gray level.

The gamma distribution is given below in Figure 5.

While the speckle noise (with variance 0.05) on an

image looks as shown in Figure 6.

Figure 5: Gamma Distribution.

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Figure 6: Image degraded by Speckle noise.

5. Restoration Algorithms

In image restoration the improvement in quality of

the restored image over the recorded blurred one is

measured by the signal-to-noise ratio improvement.

When applying restoration filters to real images of

which the ideal image is not available, often only

the visual judgement of the restored image can be

relied upon.

A. Wiener Filter

This filter can be used effectively when the

frequency characteristics of the image and additive

noise are known, to at least some degree. Wiener

filters are often applied in the frequency domain.

An important advantage of this algorithm is that it

removes the additive noise and inverts the blurring

simultaneously. A demerit of the Wiener filters is

that they are unable to reconstruct frequency

components which have been degraded by noise,

but can only suppress them. These filters are

comparatively slow to apply, since they require

working in the frequency domain. The spatially

truncated Wiener filter is inferior to the frequency

domain version, but may be much faster.

B. Regularized Filter

Regularized filtering constraints are applied on the

recovered image (e.g. smoothness) and limited

information is known about the additive noise. The

blurred and noisy image is restored by a

constrained least square restoration algorithm that

use a regularizedfilter. Although the Wiener

filtering is the optimal tradeoff of inverse filtering

and noise smoothing, in this case when the blurring

filter is singular, the Wiener filtering actually

amplify the noise.The implementation of the

regularized inverse filter involves the estimation of

the power spectrum of the original image in the

spatial domain.

C. Lucy-Richardson algorithm

The Lucy-Richardson algorithm can be used

effectively when the point-spread function PSF

(blurring operator is known, but little or no

information is available for the noise. The blurred

and noisy image is restored by the iterative,

accelerated, damped Lucy-Richardson algorithm.

The additional optical system such as camera

characteristics can be used as input parameters to

improve the quality of the image restoration. The

algorithm requires a good estimate of the process

by which the image is degraded for accurate

restoration. The degradation can be caused in many

ways, such as subject movement, out-of-focus

lenses, or atmospheric turbulence, and is described

by the point spread function (PSF) of the system.

The image is assumed to come from a Poisson

process and therefore is corrupted by signal-

dependent noise. There may also be electronic or

quantization noise involved in obtaining the image.

6. Software Algorithm

% Digital Image Processing

Clc;

Close all;

FltInitialCpuTime = cputime;

ImgTemp = imread ('Gota.jpg', 'jpg');

% Normalize Image

imgTissue1 = double (imgTemp). / 255;

%-----------------------------------------------------------

--------------------

% Part 1 - Convert image to gray level

%[X, map] = rgb2ind (imgTissue1, 256);

%imgTissue1 = ind2gray(X, map);

%imwrite (imgTissue1, 'Gota.jpg', 'jpg');

%-----------------------------------------------------------

--------------------

% Part 2 - Generation of Gaussian noise matrix

vctTissue1Size = size(imgTissue1);

MxGaussianNoise = 0.1.* randn

(vctTissue1Size (1), vctTissue1Size (2));

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%-----------------------------------------------------------

--------------------

% Part 3 - Point Spread Function (PSF)

Generation

filterPSF = fspecial('motion', 21, 11);

imgTissue1Blur = imfilter(imgTissue1,

filterPSF);

imgTissue1BlurAndNoise = imadd

(imgTissue1Blur, mxGaussianNoise);

imwrite (imgTissue1BlurAndNoise,

'Gota_blur_and_noise.jpg', 'jpg');

%-----------------------------------------------------------

--------------------

% Part 4 - Noise to Image Power Ratio

imgTissue1Spectrum =

abs(fft2(imgTissue1)).^2;

fltTissue1Power = sum

(imgTissue1Spectrum (:)) / numel

(imgTissue1Spectrum);

mxGaussianNoiseSpectrum = abs (fft2

(mxGaussianNoise)). ^2;

fltGaussianNoisePower = sum

(mxGaussianNoiseSpectrum (:)) / numel

(mxGaussianNoiseSpectrum);

fltNSR = fltGaussianNoisePower /

fltTissue1Power;

disp ('Noise to Signal Power Ratio:');

disp (fltNSR);

%-----------------------------------------------------------

--------------------

% Part 5 - Autocorrelation Functions

mxTissue1Autocorrelation =

fftshift(real(ifft2(imgTissue1Spectrum)));

mxGaussianNoiseAutocorrelation =

fftshift (real (ifft2(mxGaussianNoiseSpectrum)));

%-----------------------------------------------------------

--------------------

% Part 6 - Wiener Filtering

imgTissue1Weiner1 = deconvwnr

(imgTissue1BlurAndNoise, filterPSF);

imgTissue1Weiner2 = deconvwnr

(imgTissue1BlurAndNoise, filterPSF, fltNSR);

imgTissue1Weiner3 =

deconvwnr(imgTissue1BlurAndNoise, filterPSF,

mxGaussianNoiseAutocorrelation,

mxTissue1Autocorrelation);

figure('Name', 'Wiener Filter',

'NumberTitle', 'off', 'MenuBar', 'none');

colormap(gray);

subplot(321);

imagesc(imgTissue1);

title('Original Image');

subplot(322);

imagesc(imgTissue1BlurAndNoise);

title('Degraded Image');

subplot(323);

imagesc(imgTissue1Weiner1);

title('Default Weiner Filter with NSR =

0');

subplot(324);


title('Weiner Filter Using Noise to Signal

Ratio');

subplot(325);


title('Weiner Filter Using Autocorrelation

with NSR');

%-----------------------------------------------------------

--------------------

% Part 7 - Regularized Filtering

imgTissue1Regular1 =

deconvreg(imgTissue1BlurAndNoise, filterPSF);

imgTissue1Regular2 =

deconvreg(imgTissue1BlurAndNoise, filterPSF,

fltGaussianNoisePower); figure('Name','Regular

Filter', 'NumberTitle', 'off', 'MenuBar', 'none');

colormap(gray);

subplot(221);



subplot(222);



subplot(223);

imagesc (imgTissue1Regular1);

title('Regular Filter With No Noise

Power');

subplot(224);

imagesc(imgTissue1Regular2);

title('Regular Filter Using Noise Power');

%-----------------------------------------------------------

--------------------

% Part 8 - Lucy-Richardson Filtering

imgTissue1LucyRichardson1 =

deconvlucy(imgTissue1BlurAndNoise, filterPSF,

5);

imgTissue1LucyRichardson2 =

deconvlucy(imgTissue1BlurAndNoise, filterPSF,

3);

figure('Name', 'Lucy-Richardson Filter',

'NumberTitle', 'off', 'MenuBar', 'none');

colormap(gray);

subplot(221);



subplot(222);



subplot(223);

imagesc(imgTissue1LucyRichardson1);

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title('Lucy-Richardson Filter,

iterations=5');

subplot(224);

imagesc(imgTissue1LucyRichardson2);

title('Lucy-Richardson Filter,

iterations=3');

%-----------------------------------------------------------

--------------------

disp('CPU Time:');

disp((cputime - fltInitialCpuTime));

disp('Done.');

%-----------------------------------------------------------

--------------------

7. Simulation Results

Exploring the results of the restoration algorithms

explained in section 5 as implemented in

MATLAB.

Step 1

The original image, Gota.jpg is an RGB image and

was converted to a grayscale image using the

RGB2IND and IND2GRAY functions.

Fig.1: Original image (Gota.jpg)

Fig.2: Converted grayscale image (Gota_gray.jpg)

Step 2

A Gaussian Noise Matrix was generated using the

RANDN function. The output of the noise matrix

was intensity scaled and shown below in Figure 3.

The intensities of the image matrix were scaled

such that the highest intensity was 0.1 and the

lowest: 0.0.

Fig.3: The Gaussian Noise Matrix scaled by

intensity to 0 and 1 respectively

Step 3

A PSF was created using the FSPECIAL function

using the motionparameter. The image in Figure 2

was then motion blurred using this PSF and the

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IMFILTER function. Then, Gaussian noise was

added with the IMADD function and the Gaussian

Noise Matrix. The output of this operation on

Figure 2 is shown below:

Fig.4: Degraded image of Figure 2 using motion

blur and Gaussian noise

Step 4 The Noise to Signal Power Ratio was computed

using the following equations:

Spectrum = abs (fft2 (image)). ^2;

Power= sum (Spectrum (:)) /prod (size

(Spectrum)) ;

The equations were calculated for the image of

Figure 2 and the image of Figure 3. The powers

were then divided to get the Noise to Signal Power

Ratio. The value of which is obtained as;

Noise to Signal Power Ratio: 0.0319

Step 5

The autocorrelation matrices were computed using

the IFFT2 command. This returned the real part of

the inverse fast Fourier transforms of the spectrums

of figure 2 and figure 3. These matrices are used in

the inverse filtering of Figure4 as would be seen

later.

Step 6

The DECONVWNR function was used to perform

Wiener filtering on Figure 3. There are many

different parameters that can be used with this type

of inverse filtering. Figure 5 shows these

parameters being applied. Notice that the more

information we give the filtering function, the

better the results.

Fig.5: Results of Wiener filtering using different

parameters.

Step 7

The DECONVREG function was used to perform

Regulated filtering on Figure 3. There are many

different parameters that can be used with this type

of inverse filtering. Figure 6 shows these

parameters being applied. Notice that the more

information we give the filtering function, the

better the results. With no noise power information,

the image is heavily degraded. This is because the

filter looks at the extra noise in the image as part of

some degradation function blurring possibly and

not as additive noise.

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Fig.6: Results of Regulated filtering using different

parameters.

Step 8

The DECONVLUCY function was used to perform

Lucy-Richardson filtering on Figure 3. There are

many different parameters that can be used with

this type of inverse filtering. Figure 7 shows these

parameters being applied. Notice that as the

number of iteration we performed on the image

increased, the better quality output image was

realized. This filter is particularly interesting as it

could remove much of the blur and still leave the

noise in the image. This was not found with the two

previous filters.

Fig.7: Results of Lucy-Richardson filtering using

different parameters.

Same steps above where applied using motion blur

but with Salt and Pepper and Speckle noise models

respectively. The value of the Pepper and salt noise

models respectively. The value of 0.05 for all the

filters. Similarly, the variance v, for the speckle

noise model was set at its default value of 0.04 for

all filters. For the motion blur model, the linear

motion of the camera LEN, with the angle of

inclination THETA, were set at values of 21pixels

and 11degrees respectively.

The following results were obtained:

A.Wiener filtering of salt and pepper noise

Fig.8: Results of Wiener filtering of Salt and

Pepper noise using different parameters.

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B.Regular filtering of Salt and Pepper noise

C.Lucy-Richardson filtering of Salt and Pepper

noise

D.Wiener filtering of speckle noise

E.Regular filtering of Speckle noise

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F.Lucy-Richardson filtering of speckle noise

7. Conclusion

In conclusion, often times the colour information if

an image is irrelevant to analysis and when such is

the case, a colour image is often converted to

grayscale to speed up computation. The point-

spread function (PSF) is unknown in real life and is

often assumed based on camera parameters or other

system characteristics. It can be computed by trial

and error. However, the PSF is usually a model as

it is very complex to determine an exact

PSF.Although this paper tried exploring the effects

of other noise models, noise in an image is

commonly modelled as Gaussian. The noise to

image power ratio is good measure of how much

noise is in an image. This information, along with

the noise power, can be used in the inverse filtering

process to realize a much less degraded image. As

expected the more information you add to the

inverse filtering process, the better the output.

Inverse filtering is achieved by the use of

autocorrelation matrices that are obtained from

noise and blur information about the image. This

information expressed as a correlation is

convenient way to implement it into an inverse

filter. It can be observed from the results obtained

that with no noise information, the Wiener and

Regularized filters performance in realizing the

degraded image was poor. However, the Lucy-

Richardson filter had a good performance, despite

having no information about the noise in the image.

With noise information, the Wiener and

Regularized filters did a great job at restoring the

image. However, the Wiener filter is much better at

the blur than the Regularized filter. Despite having

no noise information, the Lucy-Richardson filter

performs rather well at removing the degradation

from the PSF (blur in the case) but not the noise.

Therefore, having a good PSF, the Wiener and

Regularized filters will perform better where the

noise information is available whereas, the Lucy-

Richardson filter performs better in blurs

elimination and not particularly the noise.

8. References

1] www.owlnet.rice.edu/elec539/projects99

[2] www.ee.un/v.edu

[3] www.gerltd.com

[4]

www.mathworks.com/help/toolbox/images/bqqhlb

w.html

[5] A.S. Awad, A Comparison between previously

known and two novel Image Restoration

Algorithms, MS Thesis, Department of Electrical &

Electronics Engineering, East Mediterranean

University. June 2001.

[6]R. L. Lagendijk and J. Biemond, Basic Methods

for Image Restoration and

Identification, Information and Communication

Theory Group, Faculty of Information Technology

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Netherlands (February, 1999).

[7] R.C. Gonzalez and R.E. Woods, Digital Image

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[8] M. Jiang and G. Wang, Development of Blind

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[9] M.R. Banham and A.K. Katsaggelos, Digital

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[12] Yung N.H.C., Lai A.H.C., Poon K.M.,

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Pan.Anoperator-splitting methodfor aliquid

crystalmodel.CompPhysComm152,2003,pp.242-

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ImageProcess,7,1998,pp.398-409,1998.

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Analysis and Comparison on Image Restoration Algorithms Using … · 2019. 7. 1. · Image restoration assures good insights of image when it is subjected to further techniques of